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SOME RESTRICTIONS ON CONSTITUTIVE EQUATIONS

In the paper, the author discusses a number of inequalities which it has been suggested, by various authors, must be satisfied by the strain-energy function for an isotropic elastic material. These include the Coleman-Noll inequality, numerous inequalities proposed by Truesdell and Toupin, the Baker-Ericksen inequality and inequalities resulting from the retirement that all speeds of propagation of waves of infinitesimal amplitude, in the statically deformed material, be real. It is shown that there is no compelling reason why the Coleman-Noll inequality or the various inequalities of Truesdell and Toupin discussed in the present paper should be satisfied. Of course, they may be satisfied for particular materials. (Author)

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Lehigh University

Center for the Application of MathematicsBethlehem, PA
United States
18015